The series tells the story of Ji Yoon-soo, a math teacher at the prestigious private Ahseong High School, known for being a hotbed of corruption. Yoon-soo is passionate about math and encourages her students to find their own answers. It is at school that she meets Baek Seung-yoo, a student who is at the bottom of the class. Seung-yoo has no friends and carries a mysterious past. As a child, he won several math Olympiads, and at age 10, he entered the Massachusetts Institute of Technology in the United States. However, he suddenly disappeared at the age of 12.
Even without many words, Seung-yoo likes to take pictures with his camera and Yoon-soo realizes its potential. With your attention, Seung-yoo's grades improve and he becomes the best student in his class. However, Yoon-soo's attention towards Seung-yoo creates rumors of a teacher-student sex scandal, resulting in her being fired.
Four years later, Yoon-soo and Seung-yoo are reunited as adults and team up to expose the corruptions present at Ahseong High School and restore Yoon-soo's reputation as a teacher.
From here there are spoilers...

So if you don't want to know more do not read!

Your last chance huh!

Ji Yoon-soo and Baek Seung-yoo meet for the first time on a train and mistakenly end up switching their belongings. To correct the mistake, they must meet and exchange their objects back. They agree to meet close to their homes to make the return. Ji Yoon-soo becomes fascinated by Baek Seung-yoo after seeing the unique photos he took. Although they may seem strange to the eyes of many, to a mathematician, they are incredible. After posing a difficult math problem that no student has been able to solve, Ji Yoon-soo discovers that someone has solved it and decides to look for the person responsible. However, due to a trauma he suffered during his time at MIT, Baek Seung-yoo doesn't want to pursue a career in mathematics and simply wants to be an ordinary student. However, when he is faced with a mathematical problem, he cannot resist the temptation to solve it.
After meeting Yoon-soo's father, a famous mathematician who went crazy trying to solve a problem, he became obsessed. Fortunately, this ended up saving his life. When he found an MIT professor, he got desperate and almost dropped out of the Olympics. However, when he finally found the solution to the problem, he killed it. Their passion for Mathematics brought them even closer, and he ended up falling in love with her.
When she discovers that the school is one of those where those who have money have power and think they can buy everything and everyone, she decides to confront Noh Jung-a (Jin Kyung), headmistress and owner of Ahsung. And then she got hurt.
The protagonist confronts the director of a school where power and money seem to buy everything, but ends up getting hurt.
The woman is a bitch, she has them all in the palm of her hand and plays with them as if they were puppets. He has cards up his sleeve and uses them according to his interests. Including Sung Ye-rin (Woo Da-vi), who is not a very good student but always gets test results to maintain her status at school.

After a study trip, they are spotted at the airport by Ye-rin. She throws the mother off so she doesn't see them (and I was thinking she was nice). But no, the little seed of evil (because the family is the root of all her problems) had an ace up her sleeve and used it against them, after being rejected by him.
On the day of Yoon-soo's wedding to her fiance, Ryo Sung-jae (Choi Dae-hoon), the image was exposed to everyone, without mercy. It was planned by Jung-a to destroy their marriage and harm Yoon-soo, causing her to lose her job and face charges of child harassment. However, on the other hand, Yoon-soo didn't love Sung-jae enough to marry him and got rid of the difficult mother-in-law.
After four years, the school has remained almost unchanged, except for the fact that Seung-yoo has turned down all job offers to prove Yoon-su's innocence regarding the charges against her.
No Jung-a will pay for all her sins with her daughter, Kim Ji-na. She steals a watch and gym project from the daughter of a woman named No Jung-a, Kim Ji-na, but Seung-yoo manages to prove that Ji-na copied Choi Si-an's work. Yoon-su and Seung-yoo are reunited and he wants to get close to her, even if she doesn't want to.
Oh, and poor Ryu Dae-hoon still has feelings for Yoon-su. Despite this, she had to move on and now she is dating Noh Yeon-woo, Jung-a's sister. He was also a victim of the snake, which only thinks of itself, and together they can make heads roll, as there is a dispute between the sisters, one owner of Ahsung Middle School and the other of Ahsung High School. And to make matters worse for Jung-a, she is an out-of-wedlock child.
Seung-yoo, determined to prove Ji Yoon-su's innocence in the episode four years ago, approaches Ye-rin and she confesses that she only sent the photo to Jung-a.
The school undergoes an audit after it is revealed that wealthy students from prominent parents were privileged in the admissions process. And the stones of the school begin to crumble. The first to fall was the corrupt teacher Han Myung-jin, who left in a rage. But he is not quiet.

Then it was her secretary who was treated like a dog. He had all the evidence against her tucked away.
Meanwhile, Yoon-su works as a tutor at a math academy, but keeps her identity a secret. But when Jung-a, the wicked snake, gets her daughter to be instructed by her, her identity is in danger of being revealed. And almost she is not discovered, but the cute Seung-yoo grabs her from behind and manages to avoid the worst.
But she can't handle the pressure, has an anxiety attack and ends up in the hospital.
Seung-yoo doesn't give up on wanting to reawaken Ji Yoon-su's love for mathematics and life, he confronts her and she collapses... on him!!! I thought there was going to be a crack there, but it wasn't this time.
Jung-a found out that Seung Yoo and Yoon-su got back together and is now sure they are behind their downfall. The woman totally freaked out and I thought it was very well done, but it won't be cheap.
But, after being humiliated by Yoon-su, Ye-rin (who I hoped had regretted it) records Seung-yoo saying he loves Yoon-su, hands it to Jung-a, who hands it to a reporter. And when Seung-yoo was entering the police station to report Jung-ah, the reporter plays the audio for everyone to hear.
It took a lot of cocoa for her, anyway, did you realize that you like Seung-yoo? She was going to do anything to protect him, but now the circus is going to catch fire, because with nothing left to lose, the two team up, with blood in their eyes, to finish her off.
But the woman has a pact with the capiroto, because no one can overthrow her. She gets the position she wanted so much, even with Professor Han testifying and the vice principal handing over the exams to Yoon-soo.
And her daughter acting up once again... It made Si-an end up in the hospital in a serious condition. But I'm sure that teacher couldn't take it anymore and told Seung-yoo that she saw Ji-na in the art room.
And I, who was rooting for Ye-rin to transform from the beginning, finally see her coming to reality and helping to prove that Yoon-soo was innocent and that the school favored upper class students.

Everyone who was humiliated by Principal Yeon-woo turned against her and helped expose the school's shenanigans, which ended up losing the title of math school.
I thought Choi Si-an was so cute with Seung-yoo and Yoon-soo at the orphanage party.
It was sad to see Yoon-soo's father go, but before that it was beautiful to see them taking the picture as a family
I just didn't understand why the director was in a wheelchair… She wasn't arrested? Did you go to an asylum?
The ending was satisfying and very rewarding. Although there may be a lot of prejudice due to the age factor, but I believe that if we look carefully, their passion was for the subject and it knew how to position itself as
Melancholia was a drama that I liked.